AC power & power factor worksheet with answers

Free printable AC power & power factor worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

New worksheet Practise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________ Date: ____________

1.Easy

A load takes 40 kW of real power and 23.5 kvar of reactive power (lagging). Find the power factor cos φ.

P = 40 kWQ = 23.5 kvar

cos φ =

2.Easy

A single-phase load connected to a 400 V supply takes 12 kW and 13.5 kvar. Find the current I drawn from the supply.

V = 400 VP = 12 kWQ = 13.5 kvar

I = A

3.Medium

A single-phase motor takes 7 kW at a power factor of 0.9 lagging from a 240 V supply. Find the line current I.

P = 7 kWpf = 0.9V = 240 V

I = A

4.Medium

Two loads are connected in parallel to a 230 V single-phase supply: a 26 kW load at a power factor of 0.65 lagging and a 21 kW load at a power factor of 0.95 lagging. Find the total current I drawn from the supply.

V = 230 VP₁ = 26 kW, pf₁ = 0.65 laggingP₂ = 21 kW, pf₂ = 0.95 lagging

I = A

5.Hard

A 200 kVA single-phase transformer supplies a load of 54 kW at a power factor of 0.8 lagging. How much extra real power ΔP can be added as a resistive (unity power factor) load before the transformer reaches its kVA rating?

S_max = 200 kVAP₁ = 54 kWpf₁ = 0.8

ΔP = kW

6.Hard

A single-phase load takes 45 kW at a power factor of 0.65 lagging from a 230 V, 50 Hz supply. A capacitor connected in parallel raises the power factor to 0.9. Find the reactive power Q_C the capacitor must supply.

P = 45 kWpf₁ = 0.65pf₂ = 0.9V = 230 Vf = 50 Hz

Q_C = kvar

Answer key

1. cos φ = 0.8622
2. I = 45.16 A
3. I = 32.41 A
4. I = 260.9 A
5. ΔP = 141.9 kW
6. Q_C = 30.82 kvar

Full step-by-step solutions: practise this topic on examproblems.com.